But Bresch argued that a lack of transparency in the complex health care system -- with bigger cuts for everyone along the supply chain -- "incentivizes higher prices" in the industry. She pointed out that copays and deductibles are on the rise, too.

Mylan responded by announcing efforts on Thursday to make EpiPen more affordable for some patients. Mylan said it will provide instant savings cards worth $300 to patients who have to pay the full price for the drug out of pocket. The move translates to about a 50% price cut for those without insurance or for patients with high deductible plans.

The controversy started with a social media movement by concerned parents who launched an online petition urging Congress to "stop the EpiPen price gouging." Eventually, more than 100,000 letters were sent to lawmakers.

The American Medical Association, which represents nearly a quarter of a million doctors, also knocked Mylan for raising the price even though the product is "unchanged" since 2009. The AMA said the "sticker shock" threatens to keep EpiPens out of reach of the people in need or force families to cut off other essentials.

Pharmacy benefit managers, which negotiate drug prices on behalf of payers like insurers, rejected Mylan's criticism of their role in the system. CEO Bresch specifically mentioned pharmacy benefit managers, along with wholesalers, as the intermediaries who have taken bigger cuts, adding to the price of the drug.

"Blaming payers for these massive price hikes is a red herring and doesn't pass the laugh test with policymakers," Mark Merritt, CEO of the Pharmaceutical Care Management Association, which represents the group, said in a statement.

The industry group compared Mylan's strategy to those pursued by Valeant(VRX) and Turing, two drug makers strongly criticized over the past year for dramatic drug price hikes. The comments came as shares of leading policy benefit managers Express Scripts(ESRX) slumped 6% on Thursday.

Bresch said she welcomes calls by members of the U.S. Senate for her to testify. The CEO said she has already reached out to a number of lawmakers, including Sen. Chuck Grassley of Iowa and Sen. Amy Klobuchar of Minnesota.

"As soon as you can meet, I'm there," Bresch said she told the senators.

The latest outraged parent is actress Sarah Jessica Parker, who had been involved in a Mylan initiative to raise awareness for anaphylaxis. But Parker announced in an Instagram post on Thursday she has ended her relationship with Mylan, saying she's "disappointed, saddened and deeply concerned" by the company's actions.